Non-parametric Tests e.g., Chi-Square

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# Non-parametric Tests e.g., Chi-Square - PowerPoint PPT Presentation

Non-parametric Tests e.g., Chi-Square. Parametric Interval or ratio data Name parametric tests we covered Tuesday. Non-parametric Ordinal and nominal data. When to use various statistics. Parametric Tests. To compare two groups on Mean Scores use t-test.

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## Non-parametric Tests e.g., Chi-Square

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### Non-parametric Testse.g., Chi-Square

Parametric

Interval or ratio data

Name parametric tests we covered Tuesday

Non-parametric

Ordinal and nominal data

When to use various statistics

Parametric Tests

To compare two groups on Mean Scores use t-test.

For more than 2 groups use Analysis of Variance (ANOVA)

Nonparametric Tests

Can’t get a mean from nominal or ordinal data.

Chi Square tests the difference in Frequency Distributions of two or more groups.

Chi-Square X2
• Chi Square tests the difference in frequency distributions of two or more groups.
• Test of Significance
• of two nominal variables or
• of a nominal variable & an ordinal variable
• Used with a cross tabulation table

2

Chi-Square

Chi-Square =

Logic of Chi-Square Analysis
• If the observed values are different enough from the expected values, you reject the null hypothesis
• If the observed values and the expected values are similar, you fail to reject the null hypothesis
Example: Work & Pregnancy
• The impact of working on pregnancy
• Ha: Working during pregnancy increases the risk of miscarriage
• H0: Working during pregnancy has NO impact on the risk of miscarriage
Example: Work & Pregnancy
• Suppose in general population 5 in 100 pregnancy results in miscarriage
• Probability(p) = .05 or 5%

Total (n=1000)

Yes

50

(5%)

No

950

(95%)

Total

1000

Example: Work & Pregnancy

Miscarriage

Work (n=500)

No Work (n=500)

Total (n=1000)

Yes

50 (5%)

No

950 (95%)

Total

500

500

100

Example: Work & Pregnancy
• H0: Working during pregnancy has NO impact on the risk of miscarriage

?

Miscarriage

Work (n=500)

No Work (n=500)

Total (n=1000)

Yes Miscarriage

25 (5%)

25

(5%)

50 (5%)

No

475 (95%)

475 (95%)

950 (95%)

Total

500

500

100

Example:Work & Pregnancy
• If NULL hypothesis TRUE, both work & no work groups would have same probability of miscarriage. EXPECTED values:

Miscarriage

Work (n=500)

No Work (n=500)

Total (n=1000)

Yes Miscarriage

40 (8%)

10

(2%)

50 (5%)

No

460 (92%)

490 (98%)

950 (95%)

Total

500

500

100

Example:Work & Pregnancy
• The actual values in your data = OBSERVED VALUES

Miscarriage

Tourist Expenditure: Mainlander vs. Japanese

Chi-Square x2= 7.34, df = 2, p<.001

Use SPSS Crosstabs (for nominal and ordinal data)
• Click…. Analyze
• Descriptive statistics
• Crosstabs
• Highlight variables for row
• Highlight variable for column
• Click statistics, click chi-square or correlation
• Etc.
• Examines if observed difference between groups in your data is true difference
• True difference = difference that exists in the population
• H0 says there is no difference in the population
Which values are compared?

Chi-Square

Frequencies in each cell

t-test

Mean and Standard Deviation of each group

If H0 is true…

Chi-Square

The values in the frequency table will look like Expected Values

t-test

The distribution of both groups will look like Population Distribution

Male

Female

Total

YES

30%

30%

30%

NO

70%

70%

70%

Total

Female

Male

t-test: If H0 is true …

# of cases

Test score

Mean

Total

Female

Male

t-test: If H0 is NOT true …

# of cases

Test score

Mean

Mean

Mean

Total

Female

Male

t-test:If H0 is NOT true …

# of cases

Test score

Mean

Mean